Math 591 - General and Differential Topology - Fall 2001
  • Time and Place:  MWF 10-11 pm in EH 2866
  • Instructor: Ralf Spatzier, 5848 East Hall, 763-2192, spatzier@math.lsa.umich.edu
  • Office Hours: Fr 11 am and 2 pm or by appointment 
  • Text:   required: ``Topology" by Munkres, 2nd edition, Prentice Hall
    • optional: ``Differential Topology'', Guillemin/Pollack, Prentice Hall 
  • Prerequisites:  Familiarity with undergraduate analysis is recommended
  • Course Outline: This course is an introduction to point set and differential topology. Specifically, we will introduce abstract topological spaces and their basic properties. Then we will discuss the properties of connectedness and compactness. We will construct new topological spaces from old ones, such as subspaces, products and quotients, group actions and orbit spaces. Finally, we will introduce manifolds and differential topology, in particular tangent spaces, the regular value theorem, Whitney's embedding theorem and transversality. Students with a strong background in point-set and differential topology may want to consider taking Math 537 instead. Math 591 will cover the prerequisites for the portions of the topology QR which concern point set topology and differential topology.
  • Problem Session: TBA
  • Grading Policy: homework 40%; midterm 30%; final exam 30%;
  • Homework Policy: Homework will be assigned weekly and collected on Friday. You may discuss the homework problems with other students, but you should write up the solutions on your own. 
  • Homeworks :You can download the homework assignments below as postscript or pdf (Adobe Acrobat) files: